A very closely related paper is [1]} which proposes the BagNet architecture. In BagNet a modified ResNet backbone is applied to each \(q\times q\)  tile of the image and the output is a class heat map. The average of these heat maps is then fed into a linear classifier. The heat maps highlight the tiles which contribute to the network's decision in a straight-forward way because of the linear classifier, improving explaininability but at the cost of some accuracy due of the modified architecture. The first main difference with our work is that, during training they consider the output of the linear classifier i.e. the weighted aggregate of the individual decisions on \(q \times q\)  tiles to be the network's prediction for the image and thus it is not directly evident what the network is considering as the labels for the individual tiles. On the other hand, we train the standard CNNs to classify each tile as belonging to its parent class making it very clear that our heat maps are the network's predictions on individual tiles. We also show using the evidence of heat maps that the CNNs trained using standard training procedures also learn the labels on tiles implicitly, thus providing explainable decisions to traditional CNN architectures without any loss of accuracy. Finally, we provide a theoretical model which explains why such a seemingly handicapped strategy can be a critical element for the success of CNNs. The theory also provides a numerical estimate for the generalization performance which correlates well with the observed test accuracies on popular data sets.
<FIGURE>